Light KK modes in Custodially Symmetric Randall-Sundrum

hep-ph/0607106, with M. Carena (FNAL), E. Pontón (Columbia) and C. Wagner (ANL)

Light KK modes in Custodially Symmetric

Randall-Sundrum

José Santiago

Theory Group (FNAL)

Motivation

Randall-Sundrum like models offer a nice solution to the gauge hierarchy problem

Bulk fermions give a rationale for fermion mass hierarchies

Fermions in Randall-Sundrum

Bulk fermions can have a mass term that determines the zero mode localization properties (and the mass of the first KK modes)

Non-trivial ( ) boundary conditions can produce ultralight KK modes (depending on the bulk mass)

zero mode

Agashe, Servant JCAP (05)

Motivation

Randall-Sundrum like models offer a nice solution to the gauge hierarchy problem

Bulk fermions give a rationale for fermion mass hierarchies

Large contributions to the parameter and force the KK modes to be too heavy to be observable at the LHC unless custodial symmetry is implemented

Outline

Custodially symmetric Randall-Sundrum models

Low energy effects of KK modes

Custodial Symmetry at work: tree-level protection ofT and

Zbb

One loop contribution to the oblique parameters

Models of gauge-Higgs unification in warped space

Realistic RS models with light KK modes: phenomenology

Summary

SU(2)L x SU(2)R Randall-Sundrum Models

Bulk gauge symmetry is broken by boundary conditions on the UV brane

where

Agashe, Delgado, May, Sundrum JHEP (03)

Low energy effects

We can integrate out the gauge KK modes in terms of the 5D propagators, with the zero mode subtracted

We will define corrections in terms of convolutions

Carena, Delgado, Pontón, Tait, Wagner PRD(03)

Low energy effects

If the light fermions are all near the UV brane we can cast the most important corrections in terms of effective oblique parameters

and the anomalous coupling

encodes the effects of gauge KK modes on decay. In practice these effects can be neglected.

If light fermions are not near the UV brane, then there are extra corrections that can be non-universal and therefore cannot be absorbed into oblique effects (more on this latter)

Carena, Delgado, Pontón, Tait, Wagner PRD(03)

Custodial symmetry at work: T and Zbb

The relevant EW observables are then the S and T oblique parameters:

and the anomalous coupling

Tend to cancel

Bad cancellationGood cancellation

Agashe, Contino, Da Rold, Pomarol ph/0605341

Quantum Numbers

or

Custodial protection of Zbb (and therefore bidoublets) is crucial to have light KK excitations

Bidoublets and oblique corrections

The new states give a one loop contribution to the parameter that is finite due to the non-local breaking of EW and

Typical results for (very sensitive to the parameters of the model and not necessarily small):

– Bidoublets contribute negatively

– Singlets and triplets contribute positively

is small and quite insensitive to the parameters of the model.

Brane Higgs

Bulk Higgs

There are regions of parameter space with a well-defined value of T:

– Negative for close to the IR brane, positive for far from the IR brane (compatible with )

heavy, small small effect from singlets

light, large large effect from singlets

Gauge-Higgs unification

We can enlarge the bulk symmetry to broken by boundary conditions to on the IR brane and to the SM on the UV brane.

The Higgs can arise then as the along the broken direction

5D gauge symmetry ensures that the Higgs potential is finite Little hierarchy

Yukawa couplings come from gauge couplings. Non-trivial flavor can be obtained by mixing at the boundary.

Agashe, Contino, Pomarol NPB(05)

Gauge-Higgs unification

Fermions must come in full representations of

We focus on the simplest realistic choice of boundary conditions and quantum numbers

With mixing

Gauge-Higgs unification

Localized masses can make the light KK modes even lighter

– Enhances the positive contribution of the singlet

– Would enhance the negative contribution of the bidoublet

The final result is similar to models with fundamental Higgs

far from the IR brane forces to be larger (to generate ) and that makes lighter and therefore its positive contribution more important

A realistic example:

– For we can get any value of T, thus the bound comes from the S parameter.

– For , the EW fit requires, at the two sigma level,

– This imposes a bound

These values can be obtained with the following parameters

Phenomenology

Fermionic spectrum:

– Three light quarks (with charge 5/3, 2/3 and -1/3) that do not mix

– Two charge 2/3 quarks that mix (strongly) with the top

– Heavier modes with masses

Top mixing with vector-like quarks induces anomalous

couplings

Moving the light generations

The S,T analysis we have performed is valid when the light quarks and leptons are near the UV brane

The couplings to the become non-universal if they get closer to the IR

A global fit is necessary in that case

Han, Skiba PRD(05); Han PRD(06); Cacciapaglia, Csaki, Marandella, Strumia ph/0604111

Conclusions

Randall-Sundrum models with custodial symmetry can have small tree-level corrections to the T parameter and the coupling.

One loop contributions to the T parameter are finite

(therefore calculable) and generically large:

– Bidoublets give a negative contribution

– Singlets and triplets give a positive contribution

Realistic models with can be constructed

and typically have light quarks that mix strongly with the top.

Exciting phenomenology at the LHC

– Light new fermions and gauge bosons

– Anomalous top couplings